共查询到20条相似文献，搜索用时 15 毫秒
1.
Several kinds of data can provide information about a variable measured on a one- or two-dimensional space; at some points, the value is known to be equal to a certain number. At other points, the only information may be that the variable is greater or smaller than a given value. The theory of splines provides interpolating functions that can take into account both equality and inequality data. These interpolating functions are presented. The parallel between splines and kriging is reviewed, using the formalism of dual kriging. Coefficients of dual kriging can be obtained directly by minimizing a quadratic form. By adding some inequality constraints to this minimization, an interpolating function may be calculated which takes into account inequality data and is more general than a spline. The method is illustrated by some simple one-dimensional examples.Work performed at Sohio Petroleum Company 相似文献
2.
A combined simulation–optimization-based methodology is proposed to identify the optimal design parameters for granular bed–stone column-improved soft soil. The methodology combines a finite difference-based simulation model and an evolutionary multiobjective optimization model. A combined simulation–optimization methodology is developed for two different formulations: (a) the minimization of maximum settlement and the minimization of differential settlement subject to stress constraints; (b) the minimization of maximum settlement, the minimization of differential settlement and the maximization of the degree of consolidation subject to stress constraints. The developed methodology is applied to an illustrative system. Different scenarios are evaluated to examine critical field conditions. The solution results show that the modular ratio and the ultimate stress carrying capacity of the stone column are the most important parameters for optimal design. The obtained results also show the potential applicability of the developed methodology. 相似文献
3.
Cost Optimization of Reinforced Earth Walls 总被引：1，自引：0，他引：1
P. K. Basudhar Amol Vashistha Kousik Deb Arindam Dey 《Geotechnical and Geological Engineering》2008,26(1):1-12
This paper deals with optimum cost (objective function) design of geosynthetic reinforced earth retaining walls subjected
to static and dynamic loading. The design restrictions are imposed as design constraints in the analysis. Choice of the initial
designed length and strength of the reinforcement, which are the elements of the design vectors are made in a way that it
forms an initial feasible design vector. Thus the problem is one of mathematical programming. The constraints and the objective
function being nonlinear in nature, the Sequential Unconstrained Minimization Technique (SUMT) has been used in conjunction
with conjugate direction and quadratic fit methods for multidimensional and unidirectional minimization to arrive at the optimal
(minimum) cost of the reinforced earth wall. Optimal cost tables are presented for different combinations of the loading and
the developed procedure is validated by taking up an example problem. It has been found from the typical example problem that
saving of the order of 7–8% can be made over the conventional design of mechanically stabilized earth (MSE) walls with the
aid of design charts. 相似文献
4.
In this contribution an algorithm for parameter identification of geometrically linear Terzaghi–Biot‐type fluid‐saturated porous media is proposed, in which non‐uniform distributions of the state variables such as stresses, strains and fluid pore pressure are taken into account. To this end a least‐squares functional consisting of experimental data and simulated data is minimized, whereby the latter are obtained with the finite element method. This strategy allows parameter identification based on in situ experiments. In order to improve the efficiency of the minimization process, a gradient‐based optimization algorithm is applied, and therefore the corresponding sensitivity analysis for the coupled two‐phase problem is described in a systematic manner. For illustrative purpose, the performance of the algorithm is demonstrated for a slope stability problem, in which a quadratic Drucker–Prager plasticity model for the solid and a linear Darcy law for the fluid are combined. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
5.
提出了一种新的波阻抗反演方法,首先根据地下反射系数序列是一个稀疏脉冲序列这一假设,将地震波阻抗反演中的目标函数表示为L1范数约束下的L1范数优化问题,并将L1范数用一个平滑函数来近似,从而使得目标函数函数可微。然后将L1范数约束下的基追踪问题转化为无约束最优化问题,并利用基于导数的局部优化方法求解无约束优化问题,求得反射系数,进而计算得到波阻抗。模型和实际资料计算结果均表明该方法可行。 相似文献
6.
Nicholas A. Teanby 《Mathematical Geosciences》2007,39(4):419-434
A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given. 相似文献
7.
Nicholas A. Teanby 《Mathematical Geology》2007,39(4):419-434
A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between
data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse
theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance
of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the
fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers.
The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example
applications to synthetic data and a record of magnetic inclination from Hawaii are given. 相似文献
8.
Thomas H. Robey 《Mathematical Geology》1995,27(6):709-729
Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches. 相似文献
9.
The present study pertains to the finding of the lower bound solution, formulating it as a non-linear programming problem using the generalized method developed by Lysmer with certain variations to incorporate the non-linear no-yield condition constraints directly in the analysis. The method considers the family of plane stress fields having the property that all stresses vary linearly within each triangular element of some mesh which covers the soil mass under study. For this type of stress field it is possible to express all equilibrium conditions as a set of linear constraints and the no-yield as a set of non-linear constraints. The boundary condition constraints may be of linear equality or inequality type. By expressing some of the design variables in terms of the remaining variables the linear equality constraints are implicity satisfied. Such a technique minimizes the complexity of the problem by eliminating the equality constraints and reduces the dimensionality of the problem, saving much, computational effort. The optimal lower bound is isolated by formulating it as a non-linear programming (NLP) problem subjected to both linear and non-linear inequality constraints. The sequential unconstrained minimization technique using the extended penalty function method as suggested by Kavlie has been used to isolate the optimal lower bound. The method has successfully been applied to the passive earth pressure and bearing capacity problem. Numerical results are obtained and compared with Lysmer's solution to show the effectiveness of the present approach. 相似文献
10.
P. Goovaerts 《Mathematical Geology》1998,30(5):511-534
This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be better conditioned to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning. 相似文献
11.
3D geological modeling should be an effective tool for accurately representing the geometric structure boundary and internal property fields of geological body. However, conventional methods have rarely focused on the expression of geological heterogeneous properties, known as 4D modeling. A volume function is defined as a piecewise mathematic function that describes a parameterized geological property field and created by fitting the property functions of certain 3D voxels. The quadratic generalized tri-prism volume function (QGTPVF) model is proposed for representing geological property fields with a sedimentary strata structure based on the volume function method and generalized tri-prism (GTP) voxel model. A QGTPVF is designed for borehole sample points, and it interpolates geological properties by fitting quadratic volume functions combined with the influence of geological geometric structure constraints, including stratum interfaces and fault planes. This research mainly focuses on the QGTPVF definition and fitting method, single GTP volume function is a continuous quadratic function, and a property smoothing along directionally adjacent bedding GTPs method is also studied, so geological property field is also expressed by the smooth function. A preprocessing method of faults geological structures is given, and the general framework QGTPVF is also discussed for practical applications. The QGTPVF model could be converted to tetrahedron voxel and 3D grid models for calculation and analysis easily. An example on a porosity property field is studied to verify the method’s accuracy and reliability by comparing to Kriging and inverse distance weighted interpolation methods, and the result of accuracy and time complexity are better, so the QGTPVF provides a new solution for modeling geological property fields. 相似文献
12.
非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。 相似文献
13.
A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young's modulus, K0 value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young's modulus and K0 are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage. 相似文献
14.
Veerle Beelaerts Maite Bauwens Emma Versteegh Frank Dehairs Rik Pintelon 《Mathematical Geosciences》2011,43(6):635-662
Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does
not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental
archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique
with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions
for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values
smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear
contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions,
and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated
on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus. 相似文献
15.
16.
When grains of a sediment sample are separated by sieving into a number of size classes, the weight of the grains belonging to a particular size-class is called the weight frequency of that class. That the weight frequencies cannot be used as simple frequencies for the calculation of the mean and standard deviation of size of grains is well known. A method is developed in this paper for estimating these two as well as a third parameter, named shape parameter, by minimizing a quadratic form that arises naturally as an analogue of the
2
statistic. Two fully worked out numerical examples, with simulated data, are presented to illustrate the method. A computer program in FORTRAN language is also appended. Comparative study shows that the quicker conventional method used by geologists may produce reasonably good estimates of standard deviation when the sample size is large, but the estimates of mean may show large deviations. 相似文献
17.
针对地震勘探中强随机噪声的去噪问题,引进支持向量回归方法,提出并证明一种新的Ricker子波核函数。支持向量回归采用核映射的基本思想,基于结构风险最小化原则,将回归问题转化为一个二次规划问题。对单道记录或多道记录中任选道的仿真实验表明,与传统的基于径向基核函数的支持向量回归及褶积滤波方法相比,使用本方法去噪后的同相轴更为清晰,波形恢复得更好,信噪比也较高,因此有可能将其应用于地震勘探记录的去噪处理中。 相似文献
18.
A new approach is proposed to simulate the daily variation of chlorophyll a in one-dimensional streams. This approach uses the plant primary production rate to quantify the phytoplankton growth rate. The delta method, which is a piecewise analytical solution technique, is applied to determine the diurnal variation in plant primary production rate. The approach is tested by applying it to the Gumsuck stream in the Kyonggi-Do province in Korea. The optimization technique with constraints is used to obtain the best running results. Application of this approach shows that the values calculated using the method presented here are in good agreement with the measured values. Therefore, we conclude that this technique realistically simulates the daily variation of chlorophyll a. 相似文献
19.
Covariance models provide the basic measure of spatial continuity in geostatistics. Traditionally, a closed-form analytical model is fitted to allow for interpolation of sample Covariance values while ensuring the positive definiteness condition. For cokriging, the modeling task is made even more difficult because of the restriction imposed by the linear coregionalization model. Bochner's theorem maps the positive definite constraints into much simpler constraints on the Fourier transform of the covariance, that is the density spectrum. Accordingly, we propose to transform the experimental (cross) covariance tables into quasidensity spectrum tables using Fast Fourier Transform (FFT). These quasidensity spectrum tables are then smoothed under constraints of positivity and unit sum. A backtransform (FFT) yields permissible (jointly) positive definite (cross) covariance tables. At no point is any analytical modeling called for and the algorithm is not restricted by the linear coregionalization model. A case study shows the proposed covariance modeling to be easier and much faster than the traditional analytical covariance modeling, yet yields comparable kriging or simulation results. 相似文献
20.
Constraining Surface Interpolations Using Elastic Plate Bending Solutions with Applications to Geologic Folding 总被引：3，自引：2，他引：1
Geologic surface interpolations can be augmented by adding physical constraints to available data. Here a method is outlined
that allows one to constrain surface interpolations for two geologic surfaces based on the apparent thickness of the bounded
layer. The resulting interpolation scheme is posed as a quadratic programming in which the interpolation of each surface is
solved approximately and subject to linear constraints on the apparent thickness. Results can be further improved by adding
cubic polynomials to the interpolating functions to regularize the problem. In one-dimensional interpolations of geologic
folds, the method improves the results over unconstrained interpolations by eliminating interpenetrations (negative apparent
thicknesses) and regions of small apparent thicknesses. In a two-dimensional application for the monocline at Raplee Ridge,
UT, the capability of this method is illustrated by overcoming interpenetration of two surfaces, the tops of the Mendenhall
oil sand and the Unnamed limestone. The minimum curvature spline interpolation is applied to topographic data taken from an
airborne laser swath mapping (ALSM) survey and interpolated by detailed geologic mapping. This method can be extended to allow
for multiple layers. 相似文献